BuildaSunFunnelforGroupViewing
oftheGreatAmericanSolarEclipse
ofAugust21,2017*
RichardTreschFienberg
AmericanAstronomicalSociety
ChuckBueter
Nightwise.org
LouisA.Mayo
NASAGoddardSpaceFlightCenter
Version3.2•June2016
*andotherfascinaJng
solarphenomena,too!
Thissimple&inexpensivedevicemakesiteasyformany
peopletoobservetheSunsimultaneously—andsafely!
OriginoftheSunFunnel:AmateurastronomersGeneZajacandChuckBueteradapted
(hAp://bit.ly/1raqocH)anexisKngdesignfora2003GreatLakesPlanetariumAssociaKon
Conferenceworkshop.Therear-screenprojecKonmaterialshownhereisanideaborrowed
fromBruceHegerberg’sSunGun(hAp://bit.ly/23SVC5N).
Contents
SafetyFirst..........................................................4
SafeSun............................................................5
Supplies&Tools..................................................... 7
MatchtheEyepiecetoYourTelescope.................................. 10
AMaAerofSize&Degrees............................................ 15
Step-by-StepAssemblyInstrucKons.....................................16
PrepareYourSunFunnel&TelescopeforUse............................33
HowtoAimaTelescopeattheSun..................................... 35
SolarFiltervs.SolarProjecKon......................................... 37
SunFunnelSafety....................................................38
AddaSolarShadetoYourSunFunnel................................... 39
WhyObservetheSun?............................................... 40
TheGalileoscope&theSunFunnel..................................... 46
MathemaKcalUnderpinningsoftheSunFunnelDesign.................... 48
ContacttheAuthors................................................. 58
SafetyFirst!
WheneveryouobservetheSun,withanytechnique,youmustputsafetyfirst.
ConstrucJonoftheSunFunnelrequirestheskilleduseofasawandother
potenJallydangeroustoolsandisthereforenotasuitableacJvityforchildren
exceptwhensupervisedcloselybyadults.
OncecompletedbyfollowingtheinstrucJonsinthisdocument,theSun
Funnelshouldbesetupbyaknowledgeableadultwhoisexperiencedinthe
useofatelescopeforsolarobserving.
ChildrenshouldneverusetheSunFunnelwithoutadultsupervision.
NeverleaveatelescopeandSunFunnel—oranyothersolar-observingsetup
—unaVended.
SafeSun
You’veprobablybeenwarnedmanyKmesnevertolookdirectlyattheSunto
avoidinjuringyoureyes.That’sgoodadvice!Also,mostcommercial
telescopeshaveasKckerwarningyounevertopointyourinstrumentatthe
Sun—again,goodadvice,notonlytoprotectyoureyesbutalsotoprotect
yourtelescope.
Butexperiencedtelescopeusersknowthatthereareatleasttwowaysto
observetheSunsafely.Oneistouseaspecial-purposeaperturefilter—that
is,afilterthatfitsovertheinstrument’saperture,orfrontopening—toblock
allbutaminusculefracKonoftheSun’slightandtherebycreatea
comfortablybrightimageinthetelescope’seyepiece.Mostsuchsolarfilters
aremadefrommetal-coatedglass,metalizedpolyesterfilm,orasheetof
black-polymermaterial.
SafeSun,ConJnued
SomeKmes,though,itcanbehardtoconvincepeopletolookthrougha
filteredtelescope;despiteyourmostsincerereassurances,they’reafraid
they’llhurttheireyes.Inanycase,onlyonepersonataKmecanviewtheSun
inthetelescope’seyepiece.
OnewayaroundtheseproblemsistoprojectanimageoftheSunfromyour
telescopeontoacardorscreen.Nownobodyhastolookthroughthe
telescope(whichmeansnorefocusingandnobumping),andmanypeoplecan
viewthesolarimageatthesameKme.Butthere’sariskthatsomeonemight
accidentallylookintothebrightbeamofsunlightemergingfromtheeyepiece.
ThesoluKontothatproblem,andanevensaferwaytouseatelescopeto
observetheSun,isrear-screenprojecKon.That’sthetechniqueusedinthe
SunFunnel.Let’sbuildone!
7
6
4
3
5
Rednumbers
correspondtoitems
listedonthenext
twopages.
8
2
9
1
Supplies&Tools
Supplies
1.Blitz/HopkinsSuperFunnel#05034,17.75-inchx5-inchx5-inch
(roundtop),$2to$6atyourlocalhardwareorauto-partsstore.
Online:hAp://amzn.to/1VzVYNP
2.Largehoseclamp,2.5-inchx5.5-inch,e.g.,Breeze#62080;$1to
$2atyourlocalhardwarestore.Online:hAp://bit.ly/qBbvRK
3.Smallhoseclamp,13/16-inchx1.5-inch,e.g.,Breeze#62016;
$0.50to$1atyourlocalhardwarestore.Online:hAp://bit.ly/oTDjRR
4.8-inchx8-inchorlargerpieceofDa-LiteHigh-ContrastDa-Tex
rear-surfaceprojecKonscreen#95774(hAp://bit.ly/1qX3yEW,$12
for1sq.r.)orCarl’sRearProjecKonFilm(hAp://amzn.to/1SsLTRN,
8½x11inchsheet,availableaspartof$3to$4samplepack).Ifyou
can’tordon’twanttobuyeithermaterial,asuitablealternaKveisto
usetwolayersofagrayorwhitevinylshower-curtainliner.
Supplies,ConJnued
5.Inexpensive(e.g.,Huygens,Kellner,Plössl)all-metal-and-glasstelescope
eyepiece,1.25-inchbarrel,focallength~5to~25mm(Kpsonchoosingthe
opKmumfocallengthfollowonsubsequentpages).Useonethatyoualready
havelyingaround,aslongasithasnoplasJcinit,whichwouldmeltorcatch
fire.Ifyoudon’thaveone,they’reavailablefromnumerousmanufacturers
anddealers—justtype“telescopeeyepieces”intoanyinternetsearch
engine,andyou’llfindmanytochoosefrom.AnothergoodsourceisSurplus
Shed(hAp://bit.ly/1SRnm2H).
Tools
6.Flat-headscrewdriver
7.Smallhacksaw
8.Medium-tofine-gritsandpaper
9.12-inchruler
MatchtheEyepiecetoYourTelescope
Whattypeoftelescope?Refractor!
Eyepiece
(noplasKc;all
metal&glass)
ObjecKve(mainlens,glass)
Stardiagonal
(noplasKc;all
metal&glass)
Photo:ExploreScienEfic
UsingaNewtonianreflectororacatadioptric(mirror-lens)
telescopeisstronglydiscouraged,asconcentratedsunlight
candestroysuchinstruments’secondary-mirrorholders.
Photo:ChuckBueter
Aperturemask
fastenedsecurely
Thatsaid,youcanuseareflectorifyou“stopdown”theapertureby
placingapieceofcardboardoverthefrontendwithasmall(1-to2inch)holecutofftoonesidetoletinonlyaliAlebitofsunlight.Besure
toinstalltheaperturemaskbeforeaimingthetelescopeattheSun!
Arefractor’sfocallengthisusuallyindicated
onthebarreloftheobjecKve(front)lensinmm.
Focallength(f)
Or,youcancalculatethefocallengthofyourtelescope
fromitsdiameter(D)andfocalraKo(f/raKoorf/number):
FLtelescope=Dtelescope×f/raJo
Example:Forthe66-mmf/5.9refractorshownonthepreviouspage,
FLtelescope=66mm×5.9=389mm(closeenough;round-offerror!)
Besteyepieceforafull-disk(~100mmdiameter)solarimage:
FLeyepiece(mm)≈FLtelescope(mm)÷43
(ThederivaEonofthisformulaappearslaterinthisdocument.)
Example:FortheGalileoscope,a50-mmf/10refractor(FLtelescope=500mm),theeyepiece
thatwillproduceafull-disksolarimagehasafocallengthofFLeyepiece=500÷43=11.6mm.
Therearemanyinexpensive12.5-mmeyepiecesavailable;anywouldmakeagoodchoice.
AneyepiecewithashorterfocallengthwillproducealargerSunimage;
aneyepiecewithalongerfocallengthwillproduceasmallerSunimage.
SamplePairsofTelescope&EyepieceFocalLengths
foraFull-DiskImageoftheSunontheSunFunnel
Telescope (FLtelescope) Eyepiece
(FLeyepiece)
300mm
400mm
500mm
600mm
700mm
800mm
900mm
1000mm
7mm
9mm
12mm
14mm
16mm
19mm
21mm
23mm
Don’tworryaboutge}ngtheeyepiecefocallength“exactlyright.”Dependingon
whatyouhaveavailableorwhatyoucanbuycheaply,aimtogetaneyepiecewhose
focallengthiswithin±10%ofthe“ideal”valueofFLtelescope÷43.
AMaVerofSize&Degrees
TheSunFunnelwasdesignedwithsmallrefractors,suchasthosewithapertures
intherangeof50to90mm(2to3½inches),inmind.There’snothingtokeep
youfromscalingituptoamuchbiggersize,exceptthatyou’relimitedbythe
amountofsunlightyoucollect,soifyoumakeamuchbiggerfunnelforasmall
refractor,you’llendupwithadisappoinKnglydimimage.
Ifyouwanttodoublethediameterofthefunnelsothatyoucandoublethe
diameterofthesolarimage,you’llneedtodoublethediameteroftherefractor
tomaintainsimilarimagebrightness.That’snottoopracKcal,assuchrefractors
aretypicallyquitelarge,heavy,andexpensive.AbeAersoluKonistousea
shorter-focal-lengtheyepiecetoincreasethemagnificaKon.Thiswillblowupthe
Sun’simagesothatit“overfills”theSunFunnelscreen,butit’llmakesunspotsor
thesilhoueAeofMercuryduringatransitappearlargerandmorevisible.
Mostrefractorsincludea90°stardiagonalwhosepurposeistomaketheviewing
anglemoreconvenient.Useit!ButiftheSunislowinthesky,it’sperfectlyOKto
leaveoutthestardiagonalandvieworproject“straightthrough”thescope.
OK,nowthatwehavealloursuppliesandtools,
includingasuitableeyepiece,let’sbuildaSunFunnel!
Step1.Thefunnelhasa
sharpliAlepieceof
plasKcprotrudingfrom
thesideabouthalfway
downitslength.
Usingthe
sandpaper,grind
itsmoothsoit
doesn’tscratch
yourhands.
Nomoresharp
pieceofplasKc!
Step2.Usingthe
hacksaw,cutthe
liAleflattaboff
thewideendof
thefunnel.
Itworksbesttocuthalfway
throughfromoneside,then
halfwaythroughfromtheother.
Roughedge!
Sanditsmooth
noworinstep5.
Step3.Usingthehacksaw,cutabout7inchesoff
thenarrowendofthefunnelsothatwhat’sler
measuresabout10incheslong(usetheruler).
7inches
s
e
h
c
n
i
10
Trytomakethecutperpendiculartotheaxisofthe
funnel,butdon’tpanicifitendsupslightlyKlted.
Rotatethefunnelasneededtocompletethecut.
Don’tbothersanding
thisroughedgeyet.
DiscardthispieceofplasKc.
Step4.Standthefunnelonits
wideend.Usingthehacksaw,cut
straightdownacrossthemiddle
ofthenarrowopening,making
yourcutabout1to2inchesdeep.
Thenarrowend
ofthefunnel
willnowhave
twosemicircles
ofplasKcrather
thanasolid
circle.
Step5.Usingthesandpaper,
smoothallthecutsurfaces
onbothendsofthefunnel.
Step6.Ifyoureyepiecehasa
rubbereyecupand/orrubber
grip,removeit/them.The
eyepieceshouldbemade
enKrelyofmetalandglass.
Notethatifyouhaveayellow
thread-ineyepiecefilter,you
canscrewitintotheeyepiece
barreltoproduceayellow
Sun.Butnote,too,thatthe
truecoloroftheSunis...
white!(Youknewthat,right?)
Step7.Inserttheeyepieceintothenarrowendofthe
funnel:lensin,chromebarrelout.Youmayneedtopry
apartthetwosemicircularhalvesofthefunnel’sopening.
Remember:Theeyepiece
mustcontainnoplasEc,
whichwouldmeltorcatch
fire.Useaneyepiecewith
onlymetalandglassparts.
IftheeyepiecesKllwon’tgoin,cut
awayaliAlemoreofthefunnelto
widentheopening,thentryagain.
Aimtogetatleastahalf
inchofthelengthofthe
eyepieceintothefunnel.
Step8.Placethesmallhoseclampoverthenarrow
endofthefunneland,usingthescrewdriver,Kghten
itaroundthefunneltosecurelyholdtheeyepiece.
Step9.Turnthefunnelwideendup(youmightfinditeasiesttositin
achairandholdthefunnelbetweenyourknees).PlacetherearprojecKonscreen(ortwolayersofvinylshower-curtainliner)overthe
wideopening;itdoesn’tmaAerwhichsidefacesdown.Lowerthe
largehoseclampoverthewideendofthefunnel...
...and,usingthescrewdriver,Kghtenitaroundthefunnelto
securelyholdthescreen;astheclampbeginstogetpurchaseonthe
funnelandscreen,gentlypulldownallaroundthelooseedgeofthe
materialsothatthescreenendsupflatandtautoverthefunnel’s
wideopening.ThisisaniteraKveprocess;you’llneedtopulldown
onthematerialarereachturnofthescrewtokeepittaut.
TheSunFunnel
CongratulaKons!YouhavesuccessfullybuiltaSunFunnel!
PrepareYourSunFunnel&TelescopeforUse
Step10.InspectyourSunFunneltomakesuretherearenoholes
intheprojecKonscreen.
ItisimportanttodothiseachandeveryKmeyougotouseyour
SunFunnel.Ifyoufindanyholesordeepscratches,youwillneed
toreplacetheprojecKonscreen.
Step11.Removeorcoveryourtelescope’sfinderscopeorreddotfinder,ifany.Brightsunlightenteringafinderscopewill
quicklymeltitscrosshairsandcouldburnanyoneoranything
posiKonedbehindit.
Ifyoucoverratherthanremoveyourfinderscopeorred-dot
finder,makesurethecoverissecureagainstwindandtheprying
fingersofsmallchildren.
Step12.WithyourtelescopeNOTpoinKngatorneartheSun,
inserttheSunFunnel’seyepiecebarrelintothe1¼-incheyepiece
holderandsecureitwiththethumbscrew(s).Thenaimyour
telescopeattheSun(seethenexttwopagesforKpsonhowto
dothis),focus,andenjoygroupviewingwithyourSunFunnel!
Cover(or
remove)your
finderscope!
Yourstardiagonalshould
containnoplasKcparts,
onlymetalandglass!
WARNING!ALWAYSSUPERVISEUSEOFTHESUNFUNNEL.NEVERPOINTAN
UNFILTEREDTELESCOPEATTHESUN.SEVEREEYEDAMAGEMAYOCCUR!
HowtoAimaTelescopeattheSun
HowdoyouaimatelescopeattheSunwhenyou’renotsupposedtolookthrough
it,andwhenyou’resupposedtoremoveorcoveryourfindersothatyoudon’t
lookthroughthateither?!
OnesoluKonistowatchyourtelescope’sshadowonthegroundandadjustthe
aimunKlthetube’sshadowisassmallandasroundasyoucangetit.
AnothersoluKonistoaddaspecial-purposeSunfinderthatprojectsashadowor
aspotofsunlightontoatarget.Thereareseveralcommercialunitsavailable,
includingthese:
•  FarLaboratoriesHelioPod:hAp://bit.ly/pcILOW
•  TeleVueSol-Searcher:hAp://bit.ly/nkhyOk
•  MeadeCoronadoSolRanger:hAp://bit.ly/1ThEIc5
YetanothersoluKonistomakesomethingyourselfbasedonthedesignofoneof
theseproducts.Seethenextpageforanexample.
Rick’shomemade
Sunfinder:Ashort
lengthofplasKc
tubingwithapiece
ofScotchMagic
Tapestuckonthe
backend.The
assemblyisaAached
withVelcroparallel
tothetelescope.
Whensunlightpours
downthetubeand
fallsonthetape,the
telescopeispointed
attheSun.Easy!
SolarFiltervs.SolarProjecJon
Ifyouhaveanaperturesolarfilterforyourtelescope,youdon’tneedaprojecKon
device—justlookthroughtheeyepiecetoseeacomfortablybrightimageofthe
Sun.Conversely,ifyouwanttouseaprojecKondevicesuchastheSunFunnel,so
thatmanypeoplecanviewtheSun’simageatthesameKme,youcan’tuseasolar
filter,becausethentheimagewouldbetoodimtoshowuponthescreen.
Whatdowemeanby“toodim”?Atypicalsolarfilterblocks99.999%oftheSun’s
light,sothattheimageintheeyepiece—orprojectedbytheeyepiece—isonly
1/100,000thasbrightasitwouldbewithoutthefilter.That’sverygoodfordirect
viewingintheeyepiece,butverybadforprojecKon.
SomesolarfiltersaremadetoshowtheSuninthelightofspecificatoms,suchas
theredlightofhydrogen(Halpha,orHα),orthevioletlightofcalcium(Ca).These
producecomfortablybrightimagesintheeyepiecebut,likefull-spectrum(“white
light”)filters,arenotsuitableforusewithprojecKonsystemsliketheSunFunnel.
SunFunnelSafety
ThekeytosuccessfulsolarprojecKon,includinguseoftheSunFunnel,istouse
therightkindoftelescope—onethatcantoleratehavingfull-strengthsunlight
passthroughtheopKcaltrain—andtouseaneyepiecethatdoesn’thaveany
plasKcinit.We’llsayitagain:Werecommendusingarefractor(atelescopewith
afrontlens)—notareflector(unlessyoustopitdowntoa1-or2-inchaperture),
andneveramirror-lenstelescope—withadecent-qualitycommercialeyepiece.
AlwaystaketheutmostcarewhenpassingunfilteredsunlightthroughanyopKcs,
asyou’lldowhenusingtheSunFunneloranyotherprojecKondevice.Ifyousee
orsmellsmoke,yourequipmentisunsuitableorsetupincorrectly—getitoutof
theSunimmediately!
DoyoursolarobservinginshortsKnts.Don’tleaveatelescopepointedattheSun
—orevensi}ngoutintheSunpointedelsewhere—forhoursataKme.And,as
notedearlier,neverleaveasolar-observingsetupunaAended.
Whenyou’refinishedwithanobservingsession,aimyourtelescopeawayfrom
theSunbeforeremovingtheSunFunnel.
AddaSolarShadetoYourSunFunnel
ToimprovetheviewontheSunFunnel’sscreen,ithelpstogetitoutofdirectsunlight.
Aneasywaytodothisistomakea“solarshade”outofa16-by-20-inchpieceofblack
foamboard,availableonline(e.g.,hAp://amzn.to/25D3CfE)oratyourlocalart-orofficesupplystore.CutaholethesamesizeasyourtelescopetubeusinganX-actoknifeand
sliptheshadeoverthetubeasshowninthephotoshere.Tip:Useyourlenscapasa
templateforthehole,butcuttheholealiAlesmallerthantheinsidediameterofthecap
sothattheboardfitssnuglyaroundthetubeandwillstaywhereyouputit.)
WhyObservetheSun?
WitheitheranaperturefilteroraprojecKonsystem,thereareallsortsof
interesKngthingstoseeontheSun,includingthese:
Sunspots.TheSunhasan11-yearmagneKc-acKvitycyclemarkedbysunspots,
darkblotchesthatarecoolerandthereforedimmerthantheirsurroundings.
Therearegenerallymoresunspotsatthepeakofthecycle,calledsolarmaximum,
andfeweratsolarminimum.Thelastmaximumwasin2014,andthenextwill
occuraround2025.Bigsunspotshaveadarkinnerpart,theumbra,andalighter
outerpart,thepenumbra,andthesecantakeonmanydifferentshapesandsizes.
SolarrotaJon.IfyouobservetheSunfromdaytoday,you’llnotethatitsrotaKon
carriessunspotsabout15°easteachday.BecausetheSunspinsonceaboutevery
25days,ittakeslessthantwoweeksfornewspotstoappearonthewesternlimb
(edge),marchacrosstheSun’sface,anddisappeararoundtheeasternlimb.
Theimagesonthenextpageshowabigsunspotoverthecourseofseveraldays.
Sunspot,
April13,2016
Umbra
Penumbra
Twodayslater
(April15)
Twodayslater
(April17)
WhyObservetheSun,ConJnued
Limbdarkening.TheouterpartsoftheSun’sdisk,towardthelimb(edge),look
darkerthanthecenter.TheSunisaballofhotgas,soitdoesn’thaveahard
surfacelikeaplanetormoon.Whenyoulooktowardthecenterofthedisk,your
gazepenetratestodeeper,hoAerlayers.Whenyoulooktowardtheedge,you’re
lookingthroughhigher,coolerlayers,whicharen’tquiteasbright.
Planetsintransit.Occasionallyoneoftheinnerplanets,VenusorMercury,
crossesinfrontoftheSunasseenfromEarth.Thisiscalledatransit,andwhenit
happens,youcanseetheplanetinsilhoueAemovingacrosstheSun’sfaceover
severalhours.VenustransitedtheSunonJune8,2004,andJune6,2012,butit
won’tdosoagainunKlDecember11,2117,soifyoumissedthelasttwo,you’re
outofluck.TransitsofMercuryaremorefrequent;recentandupcomingtransits
ofMercuryincludeNovember8,2006;May9,2016;Nov.11,2019;Nov.13,2032.
TofindoutwhentransitsofMercuryoccur,andfromwhereintheworldagiven
transitisvisible,seehAp://bit.ly/1WGafaw.
TransitofVenus:June6,2012
SizeofMercury
atsamescale:
SilhoueAe
ofVenus
Alltheseother
darksplotches
aresunspots.
NotethattheSun’slimb(edge)
islessbrightthanitscenter.
Thisiscalled“limbdarkening.”
WhyObservetheSun,ConJnued
ParJalsolareclipses.AsolareclipseoccurswhentheMoonparKallyortotally
blockstheSun.OnMonday,August21,2017,asolareclipsewillbevisible
(weatherpermi}ng)acrossallofNorthAmerica.ThewholeconKnentwill
experienceaparKaleclipselasKng2to3hours.Halfwaythroughtheevent,
anyonewithina~65-mile-widepath(hAp://bit.ly/26„ZvJ)fromOregontoSouth
Carolinawillexperienceabrieftotaleclipse,whentheMoonwillcompletelyblock
theSun’sbrightfaceforupto2minutes40seconds,turningdayintonightand
makingvisiblethespectacularcorona—theSun’setherealouteratmosphere.
LookingdirectlyattheSunissafeduringthebrieftotalphaseofasolareclipse
(“totality”),whentheMoonenKrelyblockstheSun’sbrightface.AtallotherKmes
youmustfollowthesafetyadvicethatappearsthroughoutthisdocument.TheSun
Funnelwillbeuselessduringtotality;itissuitableonlyduringtheparKalphases.
Tofindoutwhensolareclipsesoccur,andfromwhereintheworldagiveneclipse
isvisible,seehAp://bit.ly/1VFZhCz.
SolarEclipseofMarch9,2016
ObservedfromtheMoluccaSea,Indonesia
Thesequencegoesfromupper
right(beginningofeclipse)to
lowerleS(endofeclipse).
Totalsolareclipse:theonly
phaseyoucanobserve
safelywithyoureyes,i.e.,
withoutaspecial-purpose
solarfilter,aSunFunnel,or
anotherprojecKonmethod.
TheGalileoscope&theSunFunnel
TheGalileoscope(hAp://galileoscope.org)isafinetelescopetousewiththe
SunFunnel.Withsome250,000oftheseinexpensive,high-quality
telescopesinusearoundtheworld,itwouldbeashamenottousethem
forpublicviewing,forexample,duringtheparKalphasesoftheAugust21,
2017,solareclipseintheAmericas.Buttherearetwoproblems:(1)the
suppliedeyepieceisplasKcandwouldmeltifusedforsolarprojecKon,and
(2)theGalileoscopeisdesignedtobeused“straight-through,”withouta
stardiagonal,whichleavestheSunFunnel’sscreenawkwardlypointedat
theground.
Tosolvethefirstproblem,notethattheGalileoscopehasastandard1¼incheyepieceholder,soitcanusestandard1¼-inchmetaleyepieceswith
glasslenses,preferablyonewithan11-to12.5-mmfocallength.Ifyou
don’talreadyhavesuchaneyepiece,checkSurplusShedoranotherdealer.
There’snotmuchyoucandoaboutthesecondproblem,excepttoview
theSunwhenitappearslowinthesky,i.e.,intheearlymorningorlate
arernoon.AtsuchKmes,withthenearlyhorizontalGalileoscopeona
fullyextendedphototripod,theSunFunnelcanbeconvenientlyplaced
forgroupviewingoftheprojectedsolarimage.
MathemaJcalUnderpinnings
oftheSunFunnelDesign
Onthefollowingpageswegothroughthe(relaKvelysimple)math
behindtheSunFunnel.ItrelatesthefollowingquanKKesoverwhich
wehavesomemeasureofcontrol:
•  Telescopefocallength
•  Eyepiecefocallength
•  ProjecKondistance
•  Projectedimagediameter
andthefollowingquanKtyoverwhichwehaveabsolutelynocontrol:
•  Sun’sangulardiameter
Telescopeoffocallengthf(mm)producesimageof
linearsizeS(mm)ofobjectwithangularsizeA(radians).
çObjectofangularsizeA(veryfaraway)
A/2
S/2
f
A
Telescopeof
focallengthf
A/2
ImageoflinearsizeS
RelaKonshipbetweenthesequanKKes:
tan(A/2)=(S/2)/f
S/2
Rearrange tan(A/2)=(S/2)/f
toget ftan(A/2)=S/2
andfinally S=2ftan(A/2)
Notethatfortheverysmallangleswetypically
encounterinastronomy,
tan(A/2)≈A/2
sowehave S=2fA/2
whichreducesto S=fA (S,finmm;Ainradians)
WeneedtoknowthesizeoftheSunimageproduced
bythetelescope,sincethat’swhatweplantoproject
ontotheSunFunnelscreen.DoyouknowtheSun’s
angularsize,A,inradians?Probablynot,solet’s
tweakourformulatoputAintodegreesinstead.
Thereare180°inπradians(thearcofasemicircle),so
S=fA×(180°/π)
or S=fA/57.3 (Aindegrees)
TheSun’saverageangularsizeisjustover½°(you
knewthat,right?),i.e.,A≈0.533°.
So,withA=0.533°,weget
S=fA/57.3
S=f(0.533/57.3)
S=0.0093f (Sinmm,finmm)
ConsidertheGalileoscope,whichhasafocallengthof
500mm.WhenaimedattheSun,itproducesanimage
ofdiameterS=0.0093×500mm=4.65mm.
You’renotgoingtohavemuchlucktryingtosee
sunspotsorMercury’ssilhoueAeonsuchaKnyimage!
That’swhyweuseprojecKon,i.e.,toproducealarger
imageonwhichwecanmoreeasilyseesunspotsand
otherfeaturesofinterestontheSun’sdisk.
Thegeometryissimilartowhatwesawearlier:
ProjecKondistance,P
B/2
Projected
image
D/2 diameter,D
D/2
P
B/2
Angularsizeofprojectedimage,B
Eyepiece
tan(B/2)=(D/2)/P
Rearrange tan(B/2)=(D/2)/P
toget Ptan(B/2)=D/2
andfinally D=2Ptan(B/2)
Again,fortheverysmallangleswetypicallyencounterin
astronomy,
tan(B/2)≈B/2
sowehave D=2PB/2
whichreducesto D=PB (D,Pinmm;Binradians)
ButwhatisB,exactly?RememberA?It’stheangular
sizeoftheimageproducedbythetelescope.Well,B
isjustthatanglemulKpliedbythemagnificaKon
producedbythetelescope’seyepiece.Andthat,in
turn,isthefocallengthofthetelescopedividedby
thefocallengthoftheeyepiece,i.e.,
B=A×magnificaKon=A×(FLtelescope/FLeyepiece)
so D=PB
becomes D=PA(FLtelescope/FLeyepiece)
withD,P,andthetwoFL’sinmm,andAinradians.
Butremember,A(theSun’sangulardiameterinradians)
isequalto0.533/57.3,or0.0093.Soourformulaforthe
diameteroftheprojectedimage,
D=PA(FLtelescope/FLeyepiece)
becomes D=0.0093P(FLtelescope/FLeyepiece)
withallquanKKesinmm.Thiscanberearrangedtosolve
insteadfortheprojecKondistance,P:
P=107.5D(FLeyepiece/FLtelescope)
againwithallquanKKesinmm.
AlternaKvely,eitherformulacanberearrangedtosolve
insteadfortheeyepiecefocallength:
FLeyepiece=0.0093P(FLtelescope/D)
againwithallquanKKesinmm.FortheSunFunnelas
describedhere,P≈10inches≈250mm,andthe
desiredimagesizeforafull-diskSunisD≈100mm
(sincethewideendofthefunnelisabout5inches,or
127mm,across).Thus,
FLeyepiece=0.0093×254÷100×FLtelescope
or FLeyepiece=0.023FLtelescope=FLtelescope÷43
NowthatyouhaveallthemathemaKcalrelaKonshipsbetween
telescopefocallength,eyepiecefocallength,projecKondistance,
andprojectedimagesize,youcandesignyourownsolar-projecKon
deviceusingmaterialsotherthanthosesuggestedhere.
QuesJons?Comments?
Youmaycontacttheauthorsbyemail:
RickFienberg:rick.fi[email protected]
ChuckBueter:[email protected]
LouMayo:[email protected]
Exceptwhereotherwisenoted,allphotosare©2011-2016byRichardTreschFienberg.